The S&P 500 was recently up 0.5% to 1909 and earlier rose as high as 1911.

“The market is not cheap but it is not especially expensive either,” he wrote Tuesday to clients of his Westport, Conn.-based investment management and research firm. Mr. Birinyi, a long-time bull, was among a select group of Wall Streeters who called the bottom in stocks in March 2009 and has remained optimistic ever since.

Mr. Birinyi was profiled extensively in the New York Times over the weekend, saying he isn’t concerned about lackluster economic data, so-so corporate earnings and the big drop in Internet, social media and biotech stocks. In fact, he argued the gloom is actually a positive thing. “The overall market is shrugging off the tech and biotech problems, and that’s important,” he told the Times. He said stocks are in “the last stage of a great bull market. It’s the exuberant phase.”

But his latest price target is far from exuberant. The S&P 500 at 1970 would mark another 3.1% gain from current levels and an overall 6.6% gain for the year.

“Our somewhat muted outlook is in keeping with our process of deliberate, rationale forecasts,” Mr. Birinyi wrote to clients. “We have, on several occasions, compared the market to a cross country drive. To suggest that we will leave NY on Monday morning and arrive in LA mid-Saturday ignores the possibilities of detours, flat tires, bad weather and other realities.

“We are still of the belief that this market will, like others before it, end with a burst of enthusiasm, with magazine covers and with detailed stories about the stock market perhaps even making it to page on[e] now and again,” he added.